
In future wireless systems, due to privacy constraints and limited communication resources for data transmission, it is impractical for all wireless devices to transmit all of their collected data to a data center that can implement centralized machine learning algorithms for data analysis [1]}, [2]}, [3]}, [4]}, [5]}.
To this end, distributed edge learning approaches, such as federated learning (FL), were proposed [6]}, [7]}, [8]}, [9]}, [10]}, [11]}.
In FL, the wireless devices individually establish local learning models and cooperatively build a global learning model by uploading the local learning model parameters to a base station (BS) instead of sharing training data[12]}, [13]}, [14]}.
To implement FL over wireless networks, the wireless devices must transmit their local training results over wireless links [15]}, which can affect the FL performance, because both local training and wireless transmission introduce delay.
Hence, it is necessary to optimize the delay for wireless FL implementation.
